Functionally Graded Materials Research Articles

Free vibration of size-dependent FGM Mindlin microplates in viscous fluid

This paper studies the free vibration of size-dependent functionally graded material (FGM) microplates in contact with viscous fluid. The Mori-Tanaka model is applied to formulate the continuous gradual variation of material properties of FGM microplates along thickness direction. A non-classical microplate model is established based on the modified couple stress theory, which considers the size effect by introducing the material length scale parameter. A physical neutral plane is introduced to eliminate the stretching-bending coupling effect. The motion of viscous fluid is defined by Navier-Stokes equations, with which the hydrodynamic loading on microplates is determined with consideration of inertial effect and viscous damping effect. The governing equations for FGM microplates in contact with viscous fluid are derived using the Hamilton’s principle and solved by differential quadrature method. Numerical results are obtained to discuss the influences of the aspect ratio, fluid depth, slenderness ratio, fluid viscosity, gradient index, fluid density, and size parameter on the vibration behaviors of microplates in contact with viscous fluid.

Additive manufacturing of Ti-6Al-4V/V-interlayer/17-PH steel functionally graded material using angular and spheroidal V powders

The applications of V as an interlayer in functionally graded materials (FGMs) fail prematurely because of its angular shape. In this study, a radiofrequency thermal plasma process was employed to change the shape of V powder from angular to spheroidal. The angular and spheroidal V powders were then used to fabricate two FGMs, namely, Ti-6Al-4V/angular V/17-PH and Ti-6Al-4V/spherical V/17-PH. Unlike the angular V powder, the spherical V powder created a sound joint interface with a uniform layer and no cracks or delamination. The spheroidized V interlayer was thicker than the angular V interlayer. Unlike the spheroidized V interlayer, the angular V interface exhibited microcracks surrounded by σ phases. Moreover, Ti-6Al-4V/spherical V/17-PH exhibited superior mechanical properties. The high flowability associated with the fine spherical powders of Ti-6Al-4V/spherical V/17-PH significantly enhanced the efficiency of additive manufacturing and improved the microstructure and mechanical properties of the deposited joint.

Microstructure evolution and mechanical properties of functionally graded Fe–8Cr-xNi alloys fabricated by spark plasma sintering

Novel Fe–8Cr-xNi (x ε 0–9.0 wt%) functionally graded materials (FGMs) with strength gradient characteristics of ductile core and strength surface were fabricated by spark plasma sintering (SPS). Microstructure evolution and strength-toughness matching mechanism of the graded Fe–8Cr-xNi (x ε 0–9.0 wt%) alloys was investigated. Scanning electron microscopy (SEM), X-ray diffraction (XRD) and transmission electron microscopy (HR-TEM) reveal two representative areas in the microstructures evolve, i.e., an α-Fe, Ni and an α-Cr enriched white region and a remaining γ-Fe, δ-Fe and Ni enriched black region. The strength-toughness matching mechanism of composition gradient Fe–8Cr-xNi (x ε 0–9.0 wt%) alloy was that the strength of materials increased due to the formation and remain of austenitic FCC γ-Fe phase prometed by increasing Ni content, and the metallurgical bond formed among the particles. The Fe–8Cr-9.0Ni gradient layer on the surface of the SPSed gradient sample shown a highest yield strength of 150 ± 24.1 MPa and a high wear resistance of the gradient sample, and the Fe–8Cr-6.7Ni gradient layer on the middle of the sampe shown a particularly excellent ductility of 15 ± 2.1% and played a role in alleviating crack. The compressive strength of the Fe–8Cr-xNi (x ε 0–9.0 wt%) -C2 FGM alloys reaches up 3385 ± 6 MPa, and the microhardness can reach a gradient distribution of 230 ± 2, 345 ± 2 and 392 ± 1 HV from the bottom layer to the upper layer. This work provides a reliable theoretical and experimental basis for the design and application of composition gradient Fe–8Cr-xNi (x ε 0–9.0 wt%) alloys with ductile core and high strength and wear resistance surface synthesized by SPS technology.

Application of Interpolating Matrix Method to Study Dynamics of Axially Moving Beams Made of Functionally Graded Materials

In this paper, the divergent instability and coupled flutter characteristics of axially moving beams made of functionally graded materials (FGM) are studied using the interpolation matrix method. The material property of the beam is designed to change smoothly and continuously along the thickness direction. In considering the Euler-Bernoulli beam theory, Hamilton’s principle is used to derive the differential equation of the transverse vibration kinematics of axially moving FGM beams. In addition, the calculation model for solving the complex frequency of the beam based on the interpolation matrix method has been established. The presented solutions are compared with those in the literature to illustrate the effectiveness of the interpolation matrix method. The results show that the divergence and flutter velocities of axially moving FGM beams tend to decrease with the increase of the material gradient index, and there is a very narrow stability region between the first static instability region (divergence) and the first dynamic instability region (first- and second-order coupled flutter).

Nonlinear dynamic snap-through and vibrations of temperature-dependent FGM deep spherical shells under sudden thermal shock

In This article, nonlinear thermally induced vibrations of temperature-dependent functionally graded material (FGM) deep spherical shells are analyzed. One surface of the shell is kept at the reference temperature while the other one is subjected to rapid surface heating. Based on the theory of uncoupled thermoelasticity, the one-dimensional heat conduction equation across the thickness of the shell is developed and solved using the combined Crank–Nicolson method and the central finite difference method. The temperature profile obtained from the numerical solution of the heat conduction equation is used to calculate the thermal forces and the thermally induced bending moment to insert into the equations of motion of the shell. Under the assumptions of the first-order shear deformation theory (FSDT), uncoupled thermoelasticity laws, the von Kármán type of geometrical nonlinearity, and employing the Hamilton principle the axisymmetric equations of motion are obtained. The conventional multi-term polynomial Ritz method is used to discretize the governing nonlinear equations of motion. To convert the differential equations of motion into algebraic equations in each time step, the β-Newmark time marching scheme is used, and the obtained equations are solved with the help of the Newton–Raphson linearization method. In some cases, the dynamic buckling temperature is detected using the Budiansky criterion. Various numerical results are presented to analyze the effects of different parameters such as the opening angle of the shell, the thickness of the shell, and the power law index of the material composition rule.

Nonlinear dynamic snap-through and vibrations of temperature-dependent FGM deep arch under sudden thermal shock

In this paper, nonlinear thermally induced vibrations of deep arches made of functionally graded material (FGM) are investigated. The two surfaces of the arch have different thermal conditions, one surface is under thermal shock and the other is maintained at the reference temperature. The properties of FGM depend on temperature. Using the Crank–Nicolson and the central finite difference methods, the one-dimensional heat conduction equation is solved through the thickness of the arch, and the temperature profile can be obtained according to the uncoupled thermoelasticity theory. The equations of motion of the arch are extracted by combining the linear thermoelastic equation, assumptions of uncoupled thermoelasticity laws, and kinematic assumptions of a deep arch with geometrical nonlinearity. The equations of motion are discretized by using the Ritz method with polynomial shape functions and then solved with the help of the β−Newmark time marching scheme and Newton–Raphson linearization technique. The effects of various parameters such as opening angle, slenderness ratio, and arch power law index have been analyzed. Moreover, the Budiansky and other criteria are used to obtain the dynamic buckling temperature.

Interaction of Two Coaxial Penny-Shaped Cracks Near an Arbitrarily Graded Interface in Functionally Graded Materials: Exact and Approximate Solutions

Abstract Multiple cracks interaction is an important topic in fracture mechanics. The related solutions are helpful to understand the failure process and the toughening mechanism of brittle materials. Previous works on the topic were most for homogenous material. In this paper, we extend the analysis and examine the problem of interaction of two coaxial penny-shaped cracks near an arbitrarily graded interface in functionally graded materials (FGMs). The cracks are modelled as circular edge dislocation loops. An efficient dislocation solution for FGMs and Fredholm integral equation technique are used to solve the crack problem. Both exact solution using a system of integral equations and approximate solution by virtue of Kachanov’s method are presented. Unlike most existing analytical treatments to the crack problems in FGMs with the assumption of special gradation, i.e., graded shear modulus according to special functions and constant Poisson’s ratio, the present method is more flexible since it can consider arbitrarily graded shear modulus and Poisson’s ratio. The validity of the present solutions is checked by comparing to existing results in literatures for two stacked penny-shaped cracks in homogenous material and a penny-shaped crack near a graded interface with exponentially graded shear modulus. Finally, a practical example of double cracks interaction in a real epoxy-glass FGM with measured data of material properties is considered. The error due to the assumption of special gradation is also discussed.

Comparison between linear and nonlinear buckling loads of FGM cylindrical panel with cutout

This paper investigates the influences of effective parameters on the Difference between the Linear and Nonlinear Buckling Loads (DLNBL) of Functionally Graded Material (FGM) perforated cylindrical panel. In this regard, the panel was simulated using spline finite strip method. The linear and nonlinear buckling loads of the panel were obtained from linearized eigenvalue method and nonlinear geometric analysis. A comparison was made between the results obtained from the model developed in this study and those available in the literature to evaluate the validity of the results obtained from the model. Through a parametric study, the influences of different effective parameters such as cutout size, cutout shape, ratio of radius to thickness and power of FGM on the difference between the linear and nonlinear buckling loads of the panel were investigated. Although for the panels without cutout, the DLNBL was about 2 percent, it reached to 40 percent for the panels having cutout. As the cutout area increases or cutout shape changes from circle to long ellipse, the DLNBL increases significantly. Moreover, the DLNBLs obtained for shallow and FGM panels were lower than those for the deep and isotropic panels. The results obtained indicate that the buckling load obtained from linearized eigenvalue method is overestimated by about 40% for the FGM panel having long elliptical cutout. Finally, contour graphs were derived to determine the maximum difference between linear and nonlinear buckling loads of FGM panel based on the shape of cutout, size of cutout and ratio of radius to thickness of the panel. According to these graphs, the linearized eigenvalue method is not a proper method to obtain the buckling load of panels having long elliptical cutout and deep panels having medium elliptical cutout.

Dynamic Instability of Hybrid Functionally Graded Porous Plate Under Arbitrary Pulsating Loads

In this paper, the dynamic instability of hybrid functionally graded porous (FGP) plates under arbitrary periodic load is studied. The FGP plate composes of ceramic, functionally graded material (FGM) and metal. Four FGM core layers discussed include a non-pore perfect FGM layer and three imperfect FGM layers with different porosity distribution patterns. FGM layer properties are described by constituent volume fraction, porosity volume fraction and porosity distribution pattern. The Galerkin method and eigenfunctions transforms are used to establish the Mathieu-type governing equations. The influences of the load parameter, layer thickness ratio, constituent volume fraction, porosity distribution pattern and porosity volume fraction on the dynamic instability of hybrid FGP plates are investigated and discussed.

Free vibration of functionally graded sandwich plates in thermal environments

AbstractThis paper presents an analytical solution for the free vibration of functionally graded material (FGM) sandwich plates in a thermal environment. An equivalent‐single‐layer (ESL) plate theory with four variables is used to obtain the solution. Two types of sandwich plates are examined in this study: one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets. The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method. The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature. The effects of volume fraction distribution, geometrical parameters, and temperature increments on the free vibration characteristics are discussed in detail.

Buckling of Coated Functionally Graded Spherical Nanoshells Rested on Orthotropic Elastic Medium

Coated functionally graded materials (FGMs) are used in several industrial structures such as turbine blades, cutting tools, and aircraft engines. Given the need for analytical and numerical analysis of these complex structures, a mathematical model of tricoated FG structures is presented for the first time in this paper. The objective of this work was to analyze analytically the buckling problem of unidirectional (1D), bidirectional (2D), and tridirectional (3D) coated FG spherical nanoshells resting on an orthotropic elastic foundation subjected to biaxial loads. Based on the generalized field of displacement, a 2D higher-order shear deformation theory was proposed by reducing the number of displacement variables from five to four variables for specific geometry cases. The nonlocal strain gradient theory was employed to capture the size-dependent and microstructure effects. The equilibrium equations were performed by applying the principle of the virtual work, and the obtained differential equations were solved by applying the Galerkin technique to cover all possible boundary conditions. The proposed elastic foundation was defined based on three parameters: one spring constant and two shear parameters referring to the orthotropy directions. A detailed parametric analysis was carried out to highlight the impact of various schemes of coated FGMs, gradient material distribution, length scale parameter (nonlocal), material scale parameter (gradient), geometry of the nanoshell, and variation in the orthotropic elastic foundation on the critical buckling loads.

Analytical modeling of sound transmission through FGM sandwich cylindrical shell immersed in convected fluids

The main objective of this research work is focused on the acoustic response analysis of functionally graded material (FGM) sandwich cylindrical shell structure immersed in convected fluids. In the analysis, two common types of FGM sandwich cylindrical shells are considered, which include one with FGM face shell and homogeneous ceramic or metal core, and the other with FGM core and homogeneous face shell. Given the structure is immersed in a mean flowing fluid of velocity tangential to the acoustically deformed boundary and it is excited by an incidence oblique plane wave. Fluid–structure coupling is considered by imposing velocity continuity condition at fluid–structure interfaces. By comparing the numerical results with the existing solutions in open literature, the validity of the proposed theoretical model is verified. Finally, based on the developed theoretical mode, the influences of the gradient index, sandwich type, external mean flow, and skin-core-skin ratios on the structural sound transmission performance of FGM sandwich cylindrical shell have been investigated, wherein the first resonance dip shift noticeably to high frequency as the Mach number is increased, and case II has the largest amplitude fluctuation and the lowest STL curve magnitudes, in addition, when two branches, including positive refraction branch and the negative refraction branch, are found in the contour plots under opposite flow direction conditions, and the large skin-core-skin ratio is beneficial to improve the sound insulation characteristics of structures.

Functionally Gradient Material Fabrication Based on Cr, Ti, Fe, Ni, Co, Cu Metal Layers via Spark Plasma Sintering

The paper presents a method of obtaining functionally graded material (FGM) of heterogeneous (layered) type based on joined metals Cr-Ti-Fe-Co-Ni-Cu using spark plasma sintering (SPS) technology. The structure, elemental and phase composition of FGM obtained on the basis of joined metals with different values of the temperature coefficient of linear expansion (CTLE) were studied by SEM, EDS and XRD methods with regard to the phase states of the alloy system. Based on the Vickers microhardness data, the evaluation of the mechanical characteristics of FGM in the whole sample body and locally at the contact boundaries of the joined metals was carried out. The results of the study are new and represent a potential for FGM, as well as functionally graded coatings (FGC), which have special physical, chemical and mechanical properties and are highly demanded for the manufacture of structures and products for industrial applications.

Wave propagation analysis of micro air vehicle wings with honeycomb core covered by porous FGM and nanocomposite magnetostrictive layers

Recently, nano- and micro air vehicles have been intensely attractive among researchers due to their small size and ultralightweight. Hence, in this article, wave propagation of micro air vehicle wings is studied based on mathematical modeling as the main novelty of this article. In addition, assuming porous functionally graded materials (FGM) and magnetostrictive nanocomposite layers for the wing for improving the stiffness and control of the wave propagation is another important innovation of this study. The effects of size are considered based on strain gradient theory and the Halpin-Tsai model is employed for calculating the effective material characteristic of the magnetostrictive nanocomposite layer. For modeling the structure mathematically, refined zigzag theory (RZT) is used. According to Hamilton's principle, the governing equations are gained and solved by exact solutions for obtaining the phase velocity, cut-off, and escape frequencies. In this novel work, influences of dispersion kinds of GPLs, various core and face sheets thickness, damping of structure, porosity constant, FG index, auxetic honeycombs core characteristics, size parameters, and magnetic field are investigated on wave propagation of the micro air vehicle wings. It is found that by imposing the magnetic field on the magnetostrictive layer, the wave velocity is enhanced.

Effect of Functionally Graded Material (FGM) Interlayer in Metal Additive Manufacturing of Inconel-Stainless Bimetallic Structure by Laser Melting Deposition (LMD) and Wire Arc Additive Manufacturing (WAAM).

Bimetallic structures manufactured by direct deposition have a defect due to the sudden change in the microstructure and properties of dissimilar metals. The laser metal deposition (LMD)-wire arc additive manufacturing (WAAM) process can alleviate the defect between two different materials by depositing the functionally graded material (FGM) layer, such as a thin intermediate layer using LMD and can be used to fabricate bimetallic structures at high deposition rates with relatively low costs using WAAM. In this study, the LMD-WAAM process was performed, and the microstructure of the fabricated bimetallic structure of IN625-SUS304L was investigated. The microstructure of the FGM zone of the LMD-WAAM sample was mainly fine equiaxed dendrite morphologies. In contrast, coarse columnar dendrite morphologies constituted the WAAM zone. The composition of the major alloying elements of the LMD-WAAM sample gradually changed with the height of the deposited layer. The microhardness of the LMD-WAAM sample tended to increase with an increasing Inconel content. In the case of the LMD-WAAM sample, the fracture occurred near the interface between 25% IN625 and 0% IN625; in the WAAM sample, the final fracture occurred in SUS304L near the interface. The tensile strength of the LMD-WAAM samples was inversely proportional to the laser power. The results showed that the LMD-WAAM samples had 8% higher tensile strength than the samples fabricated using only WAAM.

Vibration analysis of functionally graded material (FGM) double layered floating raft structure by the spectro-geometric method

This paper aims to analyze the vibration characteristics of functionally graded material (FGM) double layered floating raft structures under various boundary conditions. The artificial virtual spring technique is introduced to simulate the boundary conditions and coupling effect between the FGM plates by adjusting the spring stiffness. The spectro-geometric method is used to describe the displacement admissible function, which overcomes the discontinuity or jump phenomenon at the boundary for the conventional Fourier series. Based on the unified Rayleigh-Ritz energy framework, the dynamic equations of the FGM double layered floating raft structure are derived, and the corresponding vibration characteristics are obtained. The correctness of the presented method is verified by some numerical examples of comparisons with the calculation results obtained from the finite element method. After that, parametric analysis is carried out to investigate the effects of material parameters, geometric parameters, coupling spring stiffness, and coupling damping on the steady-state response of the FGM double layered floating raft with various boundary conditions.

From Homogeneity to Heterogeneity: Designing Functionally Graded Materials for Advanced Engineering Applications

The research investigates Functionally Graded Materials (FGMs) and their transformational potential in modern engineering. FGMs, which exhibit progressive property fluctuations, call into question traditional material consistency. This study analyses the growth of FGMs and their importance in solving complex engineering difficulties through historical analysis and real-world case studies. The research dives into the design concepts, material selection, manufacturing procedures, and sophisticated characterisation methodologies that underpin FGM development from a methodological standpoint. Mechanical, thermal, and electrical characteristics, in combination with microstructural progression, offer a thorough knowledge of FGM behaviour. The implications for future engineering advances are highlighted, with a focus on the ability to rethink material design and multifunctional performance. Among the many attractive possibilities, issues in scalability, characterisation, and multidisciplinary cooperation need additional investigation. FGMs represent a paradigm shift from homogeneity to targeted heterogeneity, echoing wider shifts in engineering philosophy and influencing technological development.

Free vibration analysis of FGM plates and shallow shells by the R-functions method

Research of free vibration of porous functionally graded material (FGM) plates with complex shape is carried out. It is supposed that thickness of the plate changes in direction of one of the axes. Two types of porosity distributions through the thickness even and uneven are considered. Elastic foundation is two parameters (Winkler and Pasternak). To obtain the mathematical model of the given problem the first order shear deformation theory of the plate (FSDT) is used. The effective material properties in the thickness direction is modelled by the power law. Variational Ritz’s method joined with the R-functions theory is used for solution of the formulated problem. The developed approach is tested on a lot of problems. Comparative analysis of the obtained results for rectangular plates confirms their verification. Demonstration of the efficiency of the proposed approach is fulfilled for FGM plate with complex shape and various boundary conditions. Effect of the different parameters on vibration characteristics such as porosity, volume exponent, elastic foundation, types of FGM, boundary conditions is studied.

Dilatometric and microstructural study of particle and functionally graded composites based on hydroxyapatite and crystalline bioglass

Hydroxyapatite (HA) and bioglass (BG) ceramics have become of prime importance in bone tissue engineering. Besides the appropriate composition, the microstructure of bone replacement plays a crucial role. In the present work, particle composites and functionally graded material (FGM) based on HA and BG prepared by electrophoretic deposition were thoroughly characterised in terms of the preparation method, sintering process, phase composition and microstructure. The sintering was monitored by high-temperature dilatometry in two directions, the sintering rates were calculated, and the overall sintering process was discussed. The SEM showed the continuous change in the microstructure of FGM with gradual interconnected porosity favourable for bio-applications. The fundamental fractographic analysis proved the crack development in FGM related to the sintering process, and the recommendations for the reduction of the crack development were given. The phase transformations during thermal treatment were analysed using X-ray diffraction analysis and deeply discussed.

Characterization of the mechanical properties and thermal conductivity of epoxy-silica functionally graded materials

<abstract> <p>A functionally graded material (FGM) was prepared using epoxy resin reinforced with silicon dioxide with a particle size of 100 μm and weight percentages of 0, 20, 40, 60, and 80 wt%. In a gravity-molding process using the hand layup technique, specimens with international standard (ASTM)-calculated dimensions were created in a mold of poly(methyl methacrylate), which is also known as acrylic. Tensile, flexural, impact, infrared wave, and thermal conductivity tests, and X-ray diffraction (XRD) were conducted on specimens of the five layers of the FGM. The XRD and infrared spectroscopy demonstrated that the compositions of the silica particles and epoxy had a strong association with their physical structures. The findings of experimental tests indicated that increasing the ratio of silicon dioxide enhanced the mechanical properties, and the increase in modulus of elasticity was directly related to the weight percentage of the reinforcement material. The composite with 80% silica had a 526.88% higher modulus of elasticity than the pure epoxy specimen. Both tensile and flexural strengths of the composite material were maximal when 40 wt% of the particle silicon dioxide was utilized, which were 68.5% and 67.8% higher than those of the neat epoxy, respectively. The test results also revealed that the impact resistance of the FGM increased when the silica proportion increased, with a maximum value of 60 wt% silica particle content, which was an increase of 76.98% compared to pure epoxy. In addition, the thermal properties of epoxy resin improved when SiO<sub>2</sub> was added to the mixture. Thus, the addition of silica filler to composite materials directly proportionally increased their thermal conductivity to the weight ratio of the reinforcement material, which was 32.68–383.66%. FGM composed of up to 80% silica particles had the highest thermal conductivity.</p> </abstract>